Neumann-type boundary value problem associated with Hamiltonian systems
DOI:
https://doi.org/10.12775/TMNA.2023.051Keywords
Hamiltonian systems, Neumann boundary conditions, lower/upper solutions, critical point theory, Nagumo conditionAbstract
The aim of this paper is to investigate some multiplicity results for a Hamiltonian system with Neumann-type boundary conditions. A critical point theory is applied in order to show that the the problem has multiple solutions. The crucial part of this paper is that, in contrast to periodic problems where the Poincaré-Birkhoff Theorem has a significant role, no twist condition is required.References
F.H. Clarke and I. Ekeland, Nonlinear oscillations and boundary value problems for Hamiltonian systems, Arch. Rational Mech. Anal. 78 (1982), 315–333.
A. Fonda, M. Garzón and A. Sfecci, An extension of the Poincaré–Birkhoff Theorem coupling twist with lower and upper solutions, J. Math. Anal. Appl. 528 (2023), paper no. 127599, 33 pp.
A. Fonda and P. Gidoni, Coupling linearity and twist: an extension of the Poincaré–Birkhoff Theorem for Hamiltonian systems, NoDEA Nonlin. Differential Equations Appl. 27 (2020), paper no. 55, 26 pp.
A. Fonda, G. Klun, F. Obersnel and A. Sfecci, On the Dirichlet problem associated with bounded perturbations of positively-(p, q)-homogeneous Hamiltonian systems, J. Fixed Point Theory Appl. 24 (2022), paper no. 66, 32 pp.
A. Fonda, G. Klun and A. Sfecci, Well-ordered and non-well-ordered lower and upper solutions for periodic planar systems, Adv. Nonlinear Stud. 21 (2021), 397–419.
A. Fonda, N.G. Mamo, F. Obersnel and A. Sfecci, Multiplicity results for Hamiltonian systems with Neumann-type boundary conditions, NoDEA Nonlinear Differential Equations Appl. 31 (2024), paper no. 31, 30 pp.
A. Fonda and R. Ortega, A two-point boundary value problem associated with Hamiltonian systems on a cylinder, Rend. Circ. Mat. Palermo 72 (2023), 3931–3947.
A. Fonda and R. Toader, A dynamical approach to lower and upper solutions for planar systems, Discrete Contin. Dynam. Systems 41 (2021), 3683–3708.
A. Fonda and R. Toader, Subharmonic solutions of weakly coupled Hamiltonian systems, J. Dynam. Differential Equations 35 (2023), 2337–2353.
A. Fonda and W. Ullah, Periodic solutions of Hamiltonian systems coupling twist with generalized lower/upper solutions, J. Differential Equations 379 (2024), 148–174.
A. Fonda and A.J. Ureña, A higher dimensional Poincaré–Birkhoff theorem for Hamiltonian flows, Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), 679–698.
P. Gidoni, Existence of a periodic solution for superlinear second order ODEs, J. Differential Equations 345 (2023), 401–417.
J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989.
M. Nagumo, Über die Differentialgleichung y 00 = f (x, y, y 0 ), Proc. Phys.-Math. Soc. Japan 19 (1937), 861–866.
A. Szulkin, A relative category and applications to critical point theory for strongly indefinite functionals, Nonlinear Anal. 15 (1990), 725–739.
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 0
Number of citations: 0
